1. Field of the Invention
This invention relates to logging of low-frequency tube waves in boreholes, and more particularly to logging of tube waves propagated in boreholes by emission of sonic energy at discrete frequencies.
2. Description of Related Art
Emission of broad-band sonic energy in a fluid-filled tube, such as a mud-filled borehole in the earth, induces propagation of sonic waves in a number of modes. These modes include compressional, shear, and tube wave propagation.
Tube waves are a special type of surface waves. Surface waves were first postulated by Lord Rayleigh in 1885. Lord Rayleigh considered the case of a flat plane separating some solid elastic material from a vacuum, and found that the motion of the material near the plane executed a sort of elliptical motion as the surface wave passed. In 1924, R. Stoneley examined the related case in which a second solid is substituted for the vacuum, and discovered a new type of surface wave. In 1948, J. G. Scholte considered the special case when one of the materials was a fluid. The case considered by Scholte is the one of interest with respect to a fluid-filled borehole, although Stoneley's name is more commonly used in describing it.
If Scholte's plane is bent to form a cylinder, the geometry of the borehole is encountered. At very small wavelengths relative to a given borehole diameter, the cylinder will appear to the Stoneley wave as a flat plane. But with longer wavelengths, the Stoneley wave decays very little across the borehole. For example, at an operating frequency of, for example, 10 KHz, the wavelength in the mud is about 6 inches (comparable with a typical oilfield borehole diameter) and the wavelength in the formation surrounding the borehole may be as long as 2 feet. At the very low-frequency limit, the field strength of the Stoneley wave is practically flat across the borehole, since the borehole diameter is very small compared to a wavelength. Under these conditions the Stoneley wave is known as a tube wave. For purposes of the present invention and the disclosure given below, the terms "tube wave" and "Stoneley wave" will be considered synonymous.
Propagation of the tube wave up and down the borehole is believed to be affected by fluid communication between the borehole and the formation. Low-frequency tube waves have found a number of uses in borehole exploration, such as for determining formation permeability, evaluating formation fractures, and understanding rock rigidity and stress. Correlation between tube wave parameters (velocity and attenuation) and formation permeability has been reported in theory and from field data. See, for example, J. E. White, Underground Sound. pp. 139-191, Elsevier, 1983; and D. M. Williams, J. Zemanek, F. A. Angona, C. L. Dennis, and R. L. Caldwell, The Long Spaced Acoustic Logging Tool (Transactions of the SPWLA 25th Annual Logging Symposium, Paper T, 1984). The tube wave has also been used as a fracture indicator. See, for example, K. Hsu, A. Brie, and R. Plumb, A New Method for Fracture Identification Using Sonic Array Tools (Paper presented at the 1985 Annual Technical Conference and Exhibition of the Society of Petroleum Engineers of AIME, Sep. 22-25, 1985, publication no. SPE 14397). Use of tube wave information to derive the formation shear modulus is also known. See, for example, O. Y. Liu, Stoneley Wave-Derived .DELTA.t Shear Log (Paper presented at the SPWLA Twenty-Fifth Annual Logging Symposium, Jun. 10-13, 1984); and J. L. Stevens and S. M. Day, Shear Velocity Logging in Slow Formation Using the Stoneley Wave (Borehole Geophysics Abstract No. BHG7 of the Extended Abstracts of the Annual Meeting of the Society of Exploration Geophysicists, September, 1983).
Traditionally, sonic logging measurements are made in the time domain: a broad-band sonic energy source excites propagation of sonic waves in the borehole, and waveforms detected at an array of receiver locations spaced from the source in the borehole are recorded as functions of time. See, for example, D. M. Williams, J. Zemanek, F. A. Angona, C. L. Dennis, and R. L. Caldwell, The Long Spaced Acoustic Logging Tool (Transactions of the SPWLA 25th Annual Logging Symposium, Paper T, 1984). Tube wave velocity and reflection coefficients at the dominant tube wave frequency can be estimated by waveform stacking techniques, such as semblance or radon transforms.
However, quantitative interpretation and applications of the tube wave data require information about the tube waves in the frequency domain. That is, information such as tube wave velocity dispersion, tube wave attenuation and tube wave reflection coefficients are needed as functions of frequency. To obtain the frequency-dependent information, waveforms recorded in the time domain are transformed into the frequency domain before processing.
Time domain recording has several disadvantages if the frequency domain results are desired. The waveforms must be sampled in small time steps over a long period, resulting in a large set of data to transmit, store, and process. The truncation in time can cause interference in the processing. Also, the signal-to-noise ratio can be quite small for the wide-band transient measurements. The noise problem can be significant for low-frequency data (less than 500 Hz) because of the noises generated by the sonde traveling in the borehole. These problems may be avoided in accordance with the present invention by taking measurements in frequency domain.
U.S. Pat. No. 3,330,375, issued Jul. 11, 1967 to J. E. White proposes a form of acoustic well logging in which the propagation velocities of compressional, shear, mud and casing waves are determined from the expression velocity=frequency.times.wavelength by employing transmitter and/or receiver tuning techniques to determine the wavelength for a known frequency. A variety of such techniques are disclosed, involving wavelength tuning by varying frequency and/or phase shift. In all the techniques, frequency and/or phase shift is adjusted until an amplitude peak is observed, the frequencies which produce such amplitude peaks are noted, and wave propagation velocity is calculated from the expression given above. In one such technique, the wavelength of the transmitted signal is tuned to a fixed wavelength of the sending and receiving arrays by varying its frequency. In another, the wavelength of the arrays is tuned to a fixed value of the transmitted wavelength by varying the phase shift between adjacent transducer elements. In another, the frequency of the transmitted signal or the phase shift between adjacent receiving transducers, or both, are varied.
The technique of U.S. Pat. No. 3,330,375, although not directed to tube wave logging, would have the disadvantage if used for tube wave logging that insufficient information is gathered to permit derivation of both tube wave velocity and tube wave attenuation as functions of frequency. Furthermore, the disclosed method requires downhole tuning of the frequency and/or the wavelength while acquiring the data. The method is not directly applicable to obtain the frequency dependent characteristics of dispersive waves, such as the tube wave in a borehole.
In another approach, U.S. Pat. No. 4,419,748, issued Dec. 6, 1983 to R. W. Siegfried, II., proposes a continuous wave sonic logging method in which a continuous sine wave at a single frequency is emitted and received, and a spatial Fourier transform is performed over the receiver array. The resulting spatial frequency component are then used to indicate the velocities of various sonic paths. The logging method of U.S. Pat. No. 4,419,748 would have several disadvantages for tube wave logging. For example, the method requires a large number of receivers in order to facilitate the spatial Fourier transforms. Further, the disclosed method records the instantaneous values of the received signal; that is, it is recorded in time domain. Therefore, the measurement is subject to noise interferences. No improvement in the signal to noise ratio is realized by the proposed method. Furthermore, the measurement can only be done one frequency at a time (due to the time domain recording). This would require numerous logging runs for the dispersive waves, for which the wave characteristics are functions of frequency. Since the logging time is a costly factor in wire line logging services, the method is not practical for logging dispersive waves.
It is an object of the present invention to provide methods and apparatus for borehole logging with tube waves in which the aforementioned disadvantages of time-domain recording are avoided.
It is a further object of the present invention to provide methods and apparatus for borehole logging with tube waves in which the complex pressure response (amplitude and phase, or real and imaginary parts) of tube waves propagated in the borehole is detected for use in determining parameters such as tube wave phase velocity and tube wave attenuation as functions of frequency.